Large-scale photonic computing with nonlinear disordered media.

Neural networks find widespread use in scientific and technological applications, yet their implementations in conventional computers have encountered bottlenecks due to ever-expanding computational needs. Photonic computing is a promising neuromorphic platform with potential advantages of massive parallelism, ultralow latency and reduced energy consumption but mostly for computing linear operations. Here we demonstrate a large-scale, high-performance nonlinear photonic neural system based on a disordered polycrystalline slab composed of lithium niobate nanocrystals. Mediated by random quasi-phase-matching and multiple scattering, linear and nonlinear optical speckle features are generated as the interplay between the simultaneous linear random scattering and the second-harmonic generation, defining a complex neural network in which the second-order nonlinearity acts as internal nonlinear activation functions. Benchmarked against linear random projection, such nonlinear mapping embedded with rich physical computational operations shows improved performance across a large collection of machine learning tasks in image classification, regression and graph classification. Demonstrating up to 27,648 input and 3,500 nonlinear output nodes, the combination of optical nonlinearity and random scattering serves as a scalable computing engine for diverse applications.

Graph model for multiple scattering in lithium niobate on insulator integrated photonic networks.

We present a graph-based model for multiple scattering of light in integrated lithium niobate on insulator (LNOI) networks, which describes an open network of single-mode integrated waveguides with tunable scattering at the network nodes. We first validate the model at small scale with experimental LNOI resonator devices and show consistent agreement between simulated and measured spectral data. Then, the model is used to demonstrate a novel platform for on-chip multiple scattering in large-scale optical networks up to few hundred nodes, with tunable scattering behaviour and tailored disorder. Combining our simple graph-based model with material properties of LNOI, this platform creates new opportunities to control randomness in large optical networks.

Multiple Scattering and Random Quasi-Phase-Matching in Disordered Assemblies of LiNbO3 Nanocubes.

Nonlinear disordered photonic media (NDPM), composed of a random configuration of noncentrosymmetric crystals, offer a versatile platform to tailor nonlinear optical effects. The second-harmonic generation (SHG) and its random quasi-phase-matching (RQPM) in the multiple scattering regime are still poorly explored. In this work, we bottom-up assemble NDPM in two different geometries by using LiNbO3 nanocubes as building blocks and investigate both the multiple scattering and the nonlinear properties. We produce disordered slabs with a continuously variable thickness and microspheres with different diameters, which display a remarkable strong light scattering, evidenced by a subwavelength transport mean free path (). We first provide explicit evidence that the SHG power scales linearly with both the thickness of the slab and the volume of the microspheres. These observations generalize the characteristic linear scaling of RQPM power with the volume to the multiple scattering regime and to different sample geometries. Our structures represent a promising platform to investigate the interplay between disorder and optical nonlinear effects.

Invariance properties of bacterial random walks in complex structures.

Motile cells often explore natural environments characterized by a high degree of structural complexity. Moreover cell motility is also intrinsically noisy due to spontaneous random reorientations and speed fluctuations. This interplay of internal and external noise sources gives rise to a complex dynamical behavior that can be strongly sensitive to details and hard to model quantitatively. In striking contrast to this general picture we show that the mean residence time of swimming bacteria inside artificial complex microstructures is quantitatively predicted by a generic invariance property of random walks. We find that while external shape and internal disorder have dramatic effects on the distributions of path lengths and residence times, the corresponding mean values are constrained by the sole free surface to perimeter ratio. As a counterintuitive consequence, bacteria escape faster from structures with higher density of obstacles due to the lower accessible surface.

Observation of mean path length invariance in light-scattering media.

The microstructure of a medium strongly influences how light propagates through it. The amount of disorder it contains determines whether the medium is transparent or opaque. Theory predicts that exciting such a medium homogeneously and isotropically makes some of its optical properties depend only on the medium's outer geometry. Here, we report an optical experiment demonstrating that the mean path length of light is invariant with respect to the microstructure of the medium it scatters through. Using colloidal solutions with varying concentration and particle size, the invariance of the mean path length is observed over nearly two orders of magnitude in scattering strength. Our results can be extended to a wide range of systems-however ordered, correlated, or disordered-and apply to all wave-scattering problems.

Spatio-temporal visualization of light transport in complex photonic structures.

Spatio-temporal imaging of light propagation is very important in photonics because it provides the most direct tool available to study the interaction between light and its host environment. Sub-ps time resolution is needed to investigate the fine and complex structural features that characterize disordered and heterogeneous structures, which are responsible for a rich array of transport physics that have not yet been fully explored. A newly developed wide-field imaging system enables us to present a spatio-temporal study on light transport in various disordered media, revealing properties that could not be properly assessed using standard techniques. By extending our investigation to an almost transparent membrane, a configuration that has been difficult to characterize until now, we unveil the peculiar physics exhibited by such thin scattering systems with transport features that go beyond mainstream diffusion modeling, despite the occurrence of multiple scattering.

Holey random walks: optics of heterogeneous turbid composites.

We present a probabilistic theory of random walks in turbid media with nonscattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics, and void spacings can be analytically predicted. The theory is validated using Monte Carlo simulations of light transport in heterogeneous systems in the form of random sphere packings and good agreement is found. The role of step correlations is discussed and differences between unbounded and bounded systems are investigated. Our results are relevant to the optics of heterogeneous systems in general and represent an important step forward in the understanding of media with strong (fractal) heterogeneity in particular.

Weak localization of light in superdiffusive random systems.

Lévy flights constitute a broad class of random walks that occur in many fields of research, from biology to economy and geophysics. The recent advent of Lévy glasses allows us to study Lévy flights-and the resultant superdiffusion-using light waves. This raises several questions about the influence of interference on superdiffusive transport. Superdiffusive structures have the extraordinary property that all points are connected via direct jumps, which is expected to have a strong impact on interference effects such as weak and strong localization. Here we report on the experimental observation of weak localization in Lévy glasses and compare our results with a recently developed theory for multiple scattering in superdiffusive media. Experimental results are in good agreement with theory and allow us to unveil the light propagation inside a finite-size superdiffusive system.